Perturbation Methods and Semilinear Elliptic Problems on Rn

  • Antonio Ambrosetti
  • Andrea Malchiodi

Part of the Progress in Mathematics book series (PM, volume 240)

About this book

Introduction

The aim of this monograph is to discuss several elliptic problems on Rn with two main features:  they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature.
Such applications are discussed in the second part, and include semilinear elliptic
problems on Rn, bifurcation from the essential spectrum, the prescribed scalar
curvature problem, nonlinear Schrödinger equations, and singularly perturbed
elliptic problems in domains. These topics are presented in a systematic and
unified way.

Keywords

Partial differential equations Perturbation Semilinear elliptic problems compactness differential equation equation geometry partial differential equation

Authors and affiliations

  • Antonio Ambrosetti
    • 1
  • Andrea Malchiodi
    • 1
  1. 1.S.I.S.S.A.TriesteItaly

Bibliographic information

  • DOI https://doi.org/10.1007/3-7643-7396-2
  • Copyright Information Birkhäuser Verlag 2006
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7321-4
  • Online ISBN 978-3-7643-7396-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book